Error detection and correction or error control are techniques that may enable reliable delivery of digital data over unreliable communication channels and/or unreliable data storage devices. Error detection and correction belong to the field of information theory and coding theory and find application in computer science and telecommunication. Many communication channels and/or data storages may be subject to channel noise and interference, and thus errors may be introduced during transmission/storage from the source to a receiver. Error detection techniques may allow detecting such errors, while error correction may enable reconstruction of the original data. The data to be transmitted or stored may be provided, for example, in the form of binary words of a certain length.
It is known, in binary sequences or binary words of a certain length, to correct n random 1-bit errors, 2-bit errors and random 3-bit errors using BCH codes by combinational error correction circuits, as it is for example described in Okano, H. and Imai, H., “A construction method of high speed decoders using ROM's for Bose-Chadhuri-Hocquenghem and Reed Solomon Codes”, IEEE Trans. Comp. C36 (10) 1165-1175, 1987.
When BCH codes are used over a Galois field GF(2m), then n≧2m−1 and the error syndrome s may consist of 3m components, wherein the first m components may form the subsyndrome s1, the second m components the subsyndrome s3 and the third m components the subsyndrome s5, as it is common when using BCH codes. If the total parity is considered, the error syndrome may still contain a further binary component which is to be designated by sP.